But this is not ignorance. We do not know the boundaries because none have been drawn". [Wittgenstein on games] — Banno

The annoying thing, without which no threat of paradox, and everything were merely (in the current idiom) "a spectrum", is that clear enough examples of non-game are plentiful enough. (Relative to a discourse or language game, as rightly noted by @StreetlightX.)

With clear enough counter-examples, we continually imply a line, however fuzzy, even though we should admit in those cases that we are some distance from it.

Trying to approach closer to it little by little is what creates the heap paradox. Trying to define it by a formula (apart from technical contexts) is what W rightly criticizes. But acknowledging it (implicitly, behaviourally) from a distance is, I would argue, an important aspect of any game of using "game " (or other noun or adjective): an aspect which, I dare to suggest that W would agree, "never troubled you before when you used the word"(ibid), but is characteristic of that trouble-free usage.

3. Augustine, we might say, does describe a system of communica-
tion; only not everything that we call language is this system. And one
has to say this in many cases where the question arises "Is this an
appropriate description or not?" The answer is: "Yes, it is appropriate,
but only for this narrowly circumscribed region, not for the whole of
what you were claiming to describe."
It is as if someone were to say: "A game consists in moving objects
about on a surface according to certain rules . . ."—and we replied:
You seem to be thinking of board games, but there are others. You
can make your definition correct by expressly restricting it to those
games. — Philosophical Investigations

The only bit I found difficult was:
...the logic that people used in various historical periods...
— Pussycat
My predilections and prejudices pull me overwhelmingly towards coherence as a foundation to language. So I bristle at anything that might even slightly undermine that. Even though Pussycat isn't suggesting the acceptability of incoherence, I'm proceeding with exuberant caution... — Banno

I don't understand what you mean by 'coherence' as that is applied to language. But anyway, what I am saying is this: it seems to me that Wittgenstein in the Tractatus is making the correlation between language and logic, as if they were interchangeable; the limits of logic are the limits of language, and vice-versa, or maybe language delimits logic, and vice-versa, they are one and the same, let's say they are different modes of something yet unnamed. And so, an analysis or critique of language is also an analysis and critique of logic, and the opposite. Furthermore,

5.6 The limits of my language mean the limits of my world.
5.61 Logic fills the world: the limits of the world are also its limits. — w

Therefore if you want to discover what "logic people used in various historical periods", all you have to do is look at their language in that period, their world would have been limited by their employed language, mirrored by it. Which is why I said that linguists are in fact logicians, although I didn't have your average-linguist in mind when saying that, but an augmented one, the one that would trace every word, its meaning and use, back to its roots, and examine closely its evolution, why it meant what it meant then, and why did it change, under what circumstances and conditions. In all, a history of language is a history of logic.

But you can see for example our age of "political correctness", what these guys and gals are trying to do, they are trying to enforce correct use of language, eg humankind vs mankind: mankind is proscribed and condemned as a relic of a past and long-gone patriarchical civilization, something to abhor. But they are not just changing the language, but the logic of the world as well, something fundamental that is. Fascism is another example, all fascists were proud to be called so in the past, look at them now. In general: change the language, you change the logic, you change the world. But it runs bothways: recover the changes made to language, you recover a lost and obscured world.

I don't understand what you mean by 'coherence' as that is applied to language. — Pussycat

It's a family affair. There's coherence within the family. God only knows what kind of glue coheres the family. It's definitely not anything logical. So I think you're looking in the wrong direction, thinking you can determine something logical by looking at a particular group of people's use of language.

Actually, I mean lack of contradiction.

political correctness — Pussycat

Phhhht. A term invented by people who don't like being told about their prejudices.

It's a family affair. There's coherence within the family. God only knows what kind of glue coheres the family. It's definitely not anything logical. — Metaphysician Undercover

The coherence is not logical?? What then? The relations between members of the family, are they internal or external?

So I think you're looking in the wrong direction, thinking you can determine something logical by looking at a particular group of people's use of language.

According to Wittgenstein, "propositions show the logical form of reality", this is what I'm looking at here, whether it is so.

Phhhht. A term invented by people who don't like being told about their prejudices. — Banno

Regardless who or what they are, I just wanted to say that one way of imposing your worldview, would be via language, a most effective method, the reason for its effectiveness most likely being that language mirrors logic. This happens all the time in history, words are given new and different meaning, with the previous one completely shunned.

The coherence is not logical?? What then? The relations between members of the family, are they internal or external? — Pussycat

According to Wittgenstein in Philosophical investigations, a word has a family of meanings. Think of your family, the relations are external to any family member, but internal to the family as a whole. But what comprises the "whole" of your family? At some point, you need to apply some boundaries to produce that unit. But are these boundaries more than just arbitrary? The boundaries are applied for a particular purpose. When you apply the boundaries to create the unit, then the relations outside of this unit become external to that whole.

According to Wittgenstein, "propositions show the logical form of reality", this is what I'm looking at here, whether it is so. — Pussycat

Propositions are only a very small part of language use. Most language use is not a matter of making propositions. That the limits of logic are the limits of language, and that logic shows the form of reality, is the mistake which Wittgenstein made in the Tractatus, which he tried to rectify in PI.

When a word is assigned a definition in a proposition, for the purpose of a logical procedure, that definition doesn't necessarily encompass the full extent of the normal usage of that word. Because of this, the thing referred to in the proposition, by that word, may not be the same as the thing referred to by that word in common usage. This could introduce mistake into the logical process. Therefore there is a mistake in the assumption that "propositions show the logical form of reality".

3. Augustine, we might say, does describe a system of communica-
tion; only not everything that we call language is this system. And one
has to say this in many cases where the question arises "Is this an
appropriate description or not?" The answer is: "Yes, it is appropriate,
but only for this narrowly circumscribed region, not for the whole of
what you were claiming to describe."
It is as if someone were to say: "A game consists in moving objects
about on a surface according to certain rules . . ."—and we replied:
You seem to be thinking of board games, but there are others. You
can make your definition correct by expressly restricting it to those
games. — Philosophical Investigations — Metaphysician Undercover

and that logic shows the form of reality — Metaphysician Undercover

Why did you translate "propositions show the logical form of reality" into "logic shows the form of reality", it's not the same. But anyway, I doubt that later Wittgenstein changed his views on what Logic is than the tractarian one.

Why did you translate "propositions show the logical form of reality" into "logic shows the form of reality", it's not the same. But anyway, I doubt that later Wittgenstein changed his views on what Logic is than the tractarian one. — Pussycat

It's not that he changed his views on what Logic is, it's that he changed his views on reality, recognizing that there is no such thing as the logical form of reality.

It's not that he changed his views on what Logic is, it's that he changed his views on reality, recognizing that there is no such thing as the logical form of reality. — Metaphysician Undercover

Perhaps, but it would be interesting to examine this, I think, by comparing the Tractatus to the PI on this particular issue. Regretfully, I don't have enough time at the moment for a proper discussion. Anyway, I find these excerpts from the PI pertinent:

108. We see that what we call "sentence" and "language" has not the formal unity that I imagined, but is the family of structures more or less related to one another.——But what becomes of logic now? Its rigour seems to be giving way here.—But in that case doesn't logic altogether disappear?—For how can it lose its rigour? Of course not by our bargaining any of its rigour out of it.—The preconceived idea of crystalline purity can only be removed by turning our whole examination round. (One might say: the axis of reference of our examination must be rotated, but about the fixed point of our real need.)

242. If language is to be a means of communication there must be agreement not only in definitions but also (queer as this may sound) in judgments. This seems to abolish logic, but does not do so.—It is one thing to describe methods of measurement, and another to obtain and state results of measurement. But what we call "measuring" is partly determined by a certain constancy in results of measurement.

I think that Wittgenstein was afraid that if what he calls "formal unity" of language had to be dismissed, in as "there is no general form of proposition", then this would imply some bad things happening to logic as well. Also, if there is no agreement in neither definitions nor judgments, as it so happens, then this would mean that logic would have to be abolished. But it seems to me that he solves this problem by insisting on his tractarian view on logic, that it is transcendental, nothing more but just supplying the conditions for anything to be said. From 242 above, if "measurement" is the result of saying or judging something, then the fact that there is a certain constancy in it, would owe this constancy to logic, irrespective of whether someone agrees to it or not. And so, everything that we say or judge shows this transcendental logic, or Logic - in order to discriminate it from its other variations, when playing a particular language game.

The distance between the Tractatus and the Investigations is worth noting. Who else has gone so far from one point of view to another?

And if the points of view are very far apart, how will that be understood?

From a psychological perspective, the way that forms of life are presented is done with a kind of rigor that is rare. The frame is used more often than the reasoning that brought it into being.

Also, if there is no agreement in neither definitions nor judgments, as it so happens, then this would mean that logic would have to be abolished. — Pussycat

There is no need to abolish logic, only the need to see that it is not perfect or ideal. Notice the analogy with measuring. So long as we get consistency in the results, it serves the purpose. So logic is nothing other than another way of using language, if it serves the purpose, we keep doing it in a similar way, and there is consistency in the results, just like measuring. But there is nothing to indicate the logic being used, (or the system for measuring), provides the perfect or ideal way of doing things.

Cambridge Letters

Has anyone here been fortunate enough to read through this?

:brow:

Two key points, according to the article.

1. The rejection of the view of language as names and relations, in favour of language as use

2. The rejection of the private mind, hidden from public view. — Banno

Is it wrong for me to think that the term "meaning" better fits in the first? I do draw a distinction between language and meaning and I think Witt recognized this as well.

I mean, "language as use" seems to draw a false equivalence between the two, or at least suggests for one to view the former in light of the latter. Do not look for what a word means. Rather, look to how it's being used in all the common situations in which it is. Five red apples. It is in such a context that we can glean knowledge upon meaning. Also...

The tone and volume used by the speaker of a word will show us what it means. "Slab". "SLAB!". "Shut the door." "SHUT THE DOOR!"

So, I think it's safe to say that Witt knew that naming practices do not exhaust all of the ways we sensibly use language. Who ever thought or suggested that language could be properly understood solely in terms of 'names and relations'?

The private language 'argument' is convincing.

Unfortunately Witt also worked from the notion that all belief has propositional content. Hence, he struggled with all his concerted attempts to come to acceptable terms with "hinge propositions", because he was searching for rudimentary belief. He was looking to figure out how to go about determining the most basic of beliefs, the indubitable. He thought that such beliefs(hinge propositions) would somehow lie beyond the rightful applicable scope of justification. He's right about that, but it's only because that such beliefs do not have propositional content. Thus "hinge proposition" starts off on the wrong foot to begin with. As mentioned before, he followed convention on this matter, much to his own harm.

Flies in bottles is the most apt characterization that that guy penned. Shame he found himself in one with "hinge propositions".

There is no need to abolish logic, only the need to see that it is not perfect or ideal. Notice the analogy with measuring. So long as we get consistency in the results, it serves the purpose. So logic is nothing other than another way of using language, if it serves the purpose, we keep doing it in a similar way, and there is consistency in the results, just like measuring. But there is nothing to indicate the logic being used, (or the system for measuring), provides the perfect or ideal way of doing things. — Metaphysician Undercover

If Logic is what makes languages and speech possible (transcendental), then speaking any language would show and reflect it (Logic). This is what I think he meant in the Tractatus by "propositions show the logical form of reality". Coming later to the realization that (most) propositions are form-less (there is no general propositional form) and/or that language does not consist solely in propositions, he saw this as a threat to Logic, that it undermines it somehow, what happens to Logic now, he wondered. For how can you get from something that has no form - propositions - to something that has (form) - Logic? The solution was to abandon "form" altogether: Logic is still being reflected in language, sometimes having form, while other times, huh, not so much; having or not having form has nothing to do with it. The requirement of form (form and content said the german idealists, form and content he repeats in the Tractatus) in Logic and language both, but also in everything else, comes from a very long and deep tradition, this tradition that exalts "ideals" and "perfection", which is a very natural and strong tendency in all of us: the ideal way to think, the ideal way to act, to talk, to write, to make science, to philosophize, to live, to cook, to have sex etc. It seems that young Wittgenstein was caught up, like a fly, in its net, being led to dogmatism, while later he disavowed any connexions to it, the PI was an attempt to shake it off, not an easy thing to do since after two millenia it has spread its roots deep to everything. But anyway, if we would have to restate the tractarian "propositions show the logical form of reality", we could say "language shows Logic".

f Logic is what makes languages and speech possible (transcendental), then speaking any language would show and reflect it (Logic). This is what I think he meant in the Tractatus by "propositions show the logical form of reality". — Pussycat

Logic isn't what makes language possible for Wittgenstein. Perhaps he thought this when he first started to write the Tractatus, but I think he than came to recognize that logic follows from language use, as a particular type of usage. That's why he describes language in the quote you provided, as a family of structures, without formal unity. Logic is only one of the family members, one of the structures of language, there are others which we cannot call "logical".

Of course we can apply the Wittgensteinian principle I quoted above, and say that this is an unwarranted restriction of the definition of "logic", that my usage of "logic" here circumscribes a region which is not the completion of what logic really is, and claim that anything done for a reason is done logically. But then we might find "logic" within all the activities of all living things. This is the route that semiotics takes, following Peirce, and this tends to lead us into panpsychism.

So the question is how do we define "logic". If we allow that the term refers to reasoning which is other than formal logic, then we have to allow that all sorts of reasoning, thinking, and even other activities are "logical". Then we face the problem of invalid conclusions, and unreasonable thinking. Such thinking would still have to be "logical" under this extended definition, but in relation to formal logic the conclusions would be invalid, and illogical. This presents us with the appearance of a contradiction of illogical logic. But it isn't really a contradiction, because it only seems so, due to the two distinct uses of "logic", therefore that apparent contradiction is the result of equivocation. But I think it is clear from what Wittgenstein says In PI, how he defines "following a rule", that he wants to restrict "logic" to conventional forms, thereby denying such private logic (private rule following) as a form of logic.

. For how can you get from something that has no form - propositions - to something that has (form) - Logic? The solution was to abandon "form" altogether: — Pussycat

Clearly this is not a solution. The fact is that there is such a thing as formal logic. So we cannot abandon "form" altogether, in our description of language, because formality clearly enters into language use and becomes a significant part of it. So we cannot just abandon "form", and pretend that it is not there, and this is not what Wittgenstein suggested. It's more like he suggested that we put "form" in its proper place, and do not attribute to it more than what is due. I would say that he suggested that form is emergent. What you call "a threat to logic" is just the recognition of the limitations of logic, the recognition that logic is not ideal; as an emergent thing, a product of evolution, logic is limited or restricted by something larger than it. This is not a threat to logic, it is just an apprehension and understanding of the reality of what formal logic actually is.

Logic is still being reflected in language, sometimes having form, while other times, huh, not so much; having or not having form has nothing to do with it. — Pussycat

I think that this is inconsistent with PI. The family relations described cannot be said to be logical under Wittgenstein's terms. He describes a clear division between following a rule, which is the outward expression of behaving as one ought to behave, according to the rule, and the inward (family) relations of meaning which are the constituent features of language. We cannot say that these inner relations are logical because they are not rule-following relations according to Wittgenstein's terminology. Would you agree that "logic" in any sense requires some sort of rule-following?

This is where I do not agree with Wittgenstein. I think that rule-following, clearly must be brought into the internal relations, as is obvious form the observations of personal reflection. To follow a rule is to hold a principle within one's mind, which one adheres to, not to be capable of being judged as following a rule by external observation (as Wittgenstein's terminology). This is because we follow rules in thinking, whether these rules are private or not, and the private ones cannot be observed. So Wittgenstein is mistaken in his description of what it means to follow a rule, and his consequent restriction of "logic" to formal logic is also mistaken, based in this mistaken principle.

This allows for the truth of what you say, that some sort of "logic" (rule-following) is reflected in language in general, which is not necessarily formal. But this opens the can of worms, of where this rule-following activity is derived from. In saying that it underlies language, we disqualify emergence as the source of rule-following and now we are faced with the question of where does it come from. Wittgenstein has disavowed idealism by inserting a false representation of rule-following to support this disavowal. If we remove this false representation, to allow that some type of rule-following (logic) underlies all language use, as you suggest, we are thrust back toward idealism to support this underlying logic. Maintaining the disavowal leads us toward panpsychism.

Another great article from Daniele Moyal-Sharrock, which includes this concise summary of the Tractatus:

I see now that these nonsensical expressions were not nonsensical because I had not yet found the correct expressions, but that their nonsensicality was their very essence. For all I wanted to do with them was just to go beyond the world and that is to say beyond significant language. My whole tendency and, I believe, the tendency of all men who ever tried to write or talk Ethics or Religion was to run against the boundaries of language. This running against the walls of our cage is perfectly, absolutely hopeless. Ethics so far as it springs from the desire to say something about the ultimate meaning of life, the absolute good, the absolute valuable, can be no science. What it says does not add to our knowledge in any sense. (LE 44)

At this early period of his thought, Wittgenstein viewed as nonsensical any expression that did not 'add to our knowledge' that was not a proposition of natural science (6.53). The nonsensical included ethics and aesthetics (6.421), the mystical (6.522), and his own Tractarian sentences (6.54). None of these have sense – none are bipolar propositions susceptible of truth and falsity – and cannot therefore add to our knowledge. Indeed, even his Tractarian sentences do not inform; they elucidate (6.54), which is the rightful task of philosophy (4.112). It is their not adding to knowledge that makes Tractarian Sätze technically nonsensical, devoid of sense.